alg 2.
posted by Miley .
can someone please show me step by step how to do this problem...
1/2log base 4 252(3logbase4 5log base 4 25)

.5 log4 5^2 = log4(5)
2(3 log4 5  2 log4 5 ) = 2 log4 5
so we have
1 log4(5)
= log4(.2)
that might be the answer you are looking for but if you need a number
4^x = .2 ?
x ln 4 = ln .2
x = 1.39/1.61
=  .863 
I have to condense it... thanks for your help

1/2log base 4 252(3logbase4 5log base 4 25)
= 1/2 log_{4} 25  2(3log_{4} 5  log_{4} 25)
= log_{4}5  2(log_{4}125  log_{4}25)
= log_{4}5  2(log_{4}(125/25)
= log_{4}5  2log_{4}5
= log_{4}5 
my teacher has a different answer... she has log base 4(1/25).

Well, I think log4 (1/5)
I got 1 log4 5
she got 2 log4 5
one of us subtracted wrong or something
However Reiny and I agree exactly, so the odds are in our favor : 
my teacher got log base 4 (1/125) and it's a quiz review sheet, and all the math teachers look over it... sooo... I get how to simplify the 1/2 part but how do i condense the parenthesies

Well, Miley, if you typed your question correctly, then your teacher is wrong.
Even though both Damon and I did it slightly differently, we came up with the same answer.
I evaluated your original expression the way it stands on my calculator, and got the same result as our answer at the end. 
By the way, your teacher and I both said
n log4 x = log4 x^n = log4 (1/x^n)
which is how we converted the negative log to positive 
can you please show me how to condense 2(3logbase 4 5log base 4 5), thanks:)

OK, Miley, in your first post you had
...2(3logbase4 5log base 4 25)
and now you typed
...2(3logbase4 5log base 4 5)
GheeeeZZ!!!! 
Sorry it's not like i did that on purpose! Take a CHILL PILL!

I do not know what to say. Reiny and I did the parentheses quite different ways and both got the same answer.

Can you please break it down step by step and show me how you did it! thanks:)

You have two ways to condense the inside the parentheses up there
I did it by saying log 25 = 2 log 5
Reiny did it by saying
log 125  log 25 = log (125/25) = log 5 
what happen to the base 4?

What I wrote a few minutes ago is true for any old base so I left the 4 out

ohh okay thanks

2(3logbase 4 5log base 4 5)
Hey, that is not what you wrote in the original question
that is just 2 (2 log4 5)
which is
4 log4 of 5
NOW
log4 5  4 log4 5
= 3 log4 5
= log4 (1/5^3)
= log4 (1/125) 
oh my bad, sorry. wait how did you get rid of the negative two on the outside?

2(2 log) = 4 log

huh??

Uh...I'm posting this one on gothomework.tk